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An ancient north polar ocean on Mars has been proposed [Parker et al., 1989] and we use MOLA data to test the hypothesis. Of the two proposed contacts/shorelines, the younger Contact 2 shows the closest approximation to an equipotential surface; vertical variations along this surface occur in areas with post-contact-formation geological activity or suspected changes in the position of an equipotential surface (e.g., Tharsis) with time. The surface of Mars is smoother at all scales below Contact 2 than above. The volume of the region below Contact 2 (∼1.5×107 km³) is between the minimum estimated total outflow channel discharge and the maximum estimated megaregolith pore space. These results are consistent with the hypothesis that a large standing body of water occupied the northern lowlands in the past history of Mars.